MinT - Best Known (130−54, 130, s)-Nets in Base 8

Best Known (130−54, 130, s)-Nets in Base 8

(130−54, 130, 354)-Net over F₈ — Constructive and digital

Digital (76, 130, 354)-net over F₈, using

8 times m-reduction [i] based on digital (76, 138, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 69, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(130−54, 130, 476)-Net over F₈ — Digital

Digital (76, 130, 476)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−54, 130, 34778)-Net in Base 8 — Upper bound on s

There is no (76, 130, 34779)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2522 940437 906249 773451 395757 705184 360589 375435 172005 631101 459460 651716 579880 356178 260050 285755 811161 342115 598673 279160 > 8¹³⁰ [i]